Optimal. Leaf size=21 \[ \frac {5 \left (-3+e^{2+\frac {1}{x}-x \log (x)}\right )}{2 x} \]
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Rubi [A]
time = 0.07, antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps
used = 4, number of rules used = 3, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {12, 14, 2326}
\begin {gather*} \frac {5}{2} e^{\frac {1}{x}+2} x^{-x-1}-\frac {15}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{x^3} \, dx\\ &=\frac {1}{2} \int \left (\frac {15}{x^2}-5 e^{2+\frac {1}{x}} x^{-3-x} \left (1+x+x^2+x^2 \log (x)\right )\right ) \, dx\\ &=-\frac {15}{2 x}-\frac {5}{2} \int e^{2+\frac {1}{x}} x^{-3-x} \left (1+x+x^2+x^2 \log (x)\right ) \, dx\\ &=-\frac {15}{2 x}+\frac {5}{2} e^{2+\frac {1}{x}} x^{-1-x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 26, normalized size = 1.24 \begin {gather*} -\frac {5}{2} \left (\frac {3}{x}-e^{2+\frac {1}{x}} x^{-1-x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 29, normalized size = 1.38
method | result | size |
risch | \(\frac {5 x^{-x} {\mathrm e}^{\frac {2 x +1}{x}}}{2 x}-\frac {15}{2 x}\) | \(27\) |
default | \(\frac {5 \,{\mathrm e}^{\frac {-x^{2} \ln \left (x \right )+2 x +1}{x}}}{2 x}-\frac {15}{2 x}\) | \(29\) |
norman | \(\frac {-\frac {15 x}{2}+\frac {5 x \,{\mathrm e}^{\frac {-x^{2} \ln \left (x \right )+2 x +1}{x}}}{2}}{x^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 22, normalized size = 1.05 \begin {gather*} \frac {5 \, e^{\left (-x \log \left (x\right ) + \frac {1}{x} + 2\right )}}{2 \, x} - \frac {15}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 1.14 \begin {gather*} \frac {5 \, {\left (e^{\left (-\frac {x^{2} \log \left (x\right ) - 2 \, x - 1}{x}\right )} - 3\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 24, normalized size = 1.14 \begin {gather*} \frac {5 e^{\frac {- x^{2} \log {\left (x \right )} + 2 x + 1}{x}}}{2 x} - \frac {15}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.33, size = 19, normalized size = 0.90 \begin {gather*} \frac {5\,\left (\frac {{\mathrm {e}}^{\frac {1}{x}+2}}{x^x}-3\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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